NOTE: The hole at the bottom of the oil filter will appear much smaller than the shaft in the filter base - this is NORMAL and CORRECT. If you press the filter into the base, the hole will 'stretch' over the shaft. This is a design feature to ensure a tight seal so the oil does not bypass the filter.
Remember to use sythetic motor oil. MINI recommends 5W-40 or 5W-30 FULL SYNTHETIC motor oil.
To reset the oil change interval in your MINI, see oil service reset.